Actuators that can effect controlled motion in the micron or sub-micron ranges are essential components of micro-electromechanical or nano-electromechanical systems (MEMS or NEMS, respectively). In most cases, the output of an actuator is the displacement of a miniaturized suspended structure (e.g.: cantilever, membrane, rotating gear), and a variety of effects (electrostatic, piezoelectric, thermal, and magnetic) have been used successfully to transduce an input signal (usually electrical) into controllable mechanical motion. Each transducing mechanism can have advantages and disadvantages in terms of design and fabrication simplicity, control accuracy (resolution), efficiency, practical limits to motion range, and maximum operation frequency. Hence, because there is such a wide range of applications for electromechanical actuators there is no single type that is best suited for all cases. The present invention is particularly relevant for situations in which the magnitude of forces to be applied or work to be performed by the actuator is not negligible. Also, it is emphasized that only microscale applications (MEMS and NEMS) are considered in the following. Whenever the operating principles of macro actuators can be applied in scaled down versions these are also relevant. However, some of these—as for hydraulic actuators, for example—are difficult or impossible to implement in microdevices. Furthermore, the cases of higher interest here are those in which on-chip integration is feasible.
Typically, electromagnetic and magnetostatic microactuators have low output forces and displacements. This is due to the fact that the forces induced by magnetic fields scale down very rapidly with size. The prior art has reported currents of 80 mA that have generated 200 μN of actuation force and bending displacements of 50 μm. The size of such device was about 8 mm2. Another spiral-type magnetic microactuator has been reported of being capable of producing forces of 1.24 mN, with displacements up to 28 μm. However, this device still had dimensions in the millimeter range. An additional limitation is that electromagnetic and magnetostatic actuators usually need an excitation source external to the chip where the device is located, impeding their complete integration into one single chip.
Micrometer sized electrostatic actuators use the attractive or repelling force between two changed plates or surfaces. These can sustain very high electric fields when fabricated in the micrometer scale, since the gaps between the charged surfaces can be smaller than the mean free path of electrons in air at room temperature (˜6 μm). Electrostatic comb-drives have been actuated with 20 V and achieved displacements close to 30 μm. Later improvements in the design and fabrication led to displacements of up to 150 μm in 1 ms on comb-drive devices actuated with 150 V. Combdrives are usually the type of devices used for actuating micro engines. Although relatively large torqueses have been delivered, because the gear movement is rotational (angular motion), the linear displacements have been close to 40 μm. However, other types of electrostatic actuators, such as scratch drives and impact actuators can be used to obtain deflections as large as 200 μm. Impact actuators need multiple motions (or impacts) in order to produce a total displacement in the micrometer range, and total device sizes are several mm. Scratch drive actuators are also usually operated by an AC voltage and can supply forces close to 1 mN and have displacements close to 200 μm.
Piezoelectric actuators can produce forces up to ˜1 mN and displacements up to ˜200 μm, although due to materials characteristics a compromise between high forces and long displacements must be made. Mechanically amplified piezoelectric actuators can provide displacements up to 1.2 mm, but at the cost of reduced usable force. Also, piezoelectric actuators that can provide such large displacements have dimensions in the millimeter range. A clear advantage of piezoelectrics is their capability for very fast response, which extends to nearly 10 kHz, and can be increased by up to two orders of magnitude in piezoelectric “bimorph” cantilever geometries—albeit with a substantial reduction in the useful force. One disadvantage of piezoelectric actuators is that materials with optimal characteristics are themselves relatively complex compounds, which may not be easily deposited as thin films with standard microfabrication technology. Another difficulty is the need for relatively high operation voltages, which can hinder applicability in MEMS and NEMS.
The family of thermal actuators can be divided in several classes according to the phenomenon caused by the change in temperature. Some of these, such as thermopneumatics, require relatively complex fabrication and operation and are less suitable for miniaturization and on-chip integration. In this regard, the most promising classes of thermal actuators for integration in MEMS and NEMS, and able to provide adequate forces and displacements in at least a variety of applications are those based on solid expansion, particularly trough differences in thermal expansion, and on the shape memory effect. The latter is due to a reversible martensitic transformation occurring in alloys such as Ni—Ti, and is the mechanism behind shape memory alloy (SMA) actuators. Among all the types of mechanical actuators they currently offer the highest work per unit volume. Many SMA materials are relatively easy to deposit as thin films with standard techniques, which simplifies their application in microdevices. Over a decade ago the dimensions of the smallest SMA-based devices were in the millimeter range and their reported displacements were not larger than 35 μm. However, in recent years smaller devices capable of displacements of over 100 μm have been demonstrated.
The other main class of thermal actuators suitable for miniaturization and large-scale integration uses the mechanism of thermal expansion coefficient differential (TECD) of two materials (Δα=αa−αb). These actuators are basically released structures (e.g., cantilevers) made out of at least two different materials with different thermal expansion coefficients (αa, αb). When heated, the difference in the thermal expansion coefficients causes the layers to expand at different rates. The stress developed causes the cantilever to bend in a direction perpendicular to the plane of the layers, with the layer with the lowest thermal expansion coefficient facing the inner side of the arc formed by the cantilever. Finite element methods have been used to optimize the actuator geometry for maximum deflections on TECD actuators about 150 μm long and 50 μm wide, but no deflections larger than 20 μm were obtained. The largest displacements achieved so far with bi-material cantilevers using the TECD mechanism have been obtained by using polymides to coat a ceramic cantilever. This arrangement takes advantage of the large difference in thermal expansion coefficients between the polymide (large α) and the ceramic (small α). Tip deflections up to 50 μm have been obtained in ˜300 μm long cantilevers. However, large temperature increases e required in order to achieve them, which imposes demands on designs to reduce thermal losses through conduction. Moreover, because polymers have a relatively low melting temperature, the maximum temperature differential applicable in such devices is limited. Finally, as discussed later, the forces exerted by these polymide-coated cantilevers are relatively small. These facts imply that their usefulness is mainly as sensor devices, not as actuators.
The cantilevered bi-material strip just described can use not just TEDC as the working mechanism but also the shape memory effect or indeed any mechanism that will create a stress between the two layers. While this actually includes the piezoelectric effect, the following will consider only thermally activated mechanisms. Two important performance parameters which should be specified when comparing bi-material cantilever devices of this type is the curvature change produced over a specified temperature change, and the recoverable work per unit volume performed over this temperature interval. Cantilever tip deflections are often quoted for specific devices, but these are a function of cantilever length. Curvature change is independent of length and therefore is a better measure of the obtainable performance for a pair of materials. In the case of interest for microdevice actuators one of the two materials is commonly a relatively thick substrate and the other is a relatively thin film which coats the substrate. Bending of the bi-material cantilever is caused by film stress, whose magnitude (σf) can be estimated from the formula:
                                          σ            f                    =                                    (                                                                    t                    2                    3                                    ⁢                                      E                    s                                                                    6                  ⁢                                                            t                      f                      2                                        ⁡                                          (                                              1                        -                                                  v                          s                                                                    )                                                        ⁢                  R                                            )                        ⁢                          1                              1                +                B                                                    ,                            (        1        )            where tf is the film thickness and ts, Es, and νs are the substrate's thickness, Young's modulus, and Poisson's ratio, respectively, while B=tf/ts is the thickness ratio between film and substrate.
Equation (1) is a better approximation than the well-known Stoney's formula when film thickness is not negligible in comparison with that of the substrate.
The curvature κ (i.e., the inverse of the radius of curvature) of a bilayered cantilever with rectangular cross section can be calculated from the expression:
                                          κ            ≡                          1              R                                =                                                    6                ⁢                                                      (                                          1                      +                      B                                        )                                    2                                ⁢                ɛ                                            t                ⁡                                  [                                                            3                      ⁢                                                                        (                                                      1                            +                            B                                                    )                                                2                                                              +                                                                  (                                                  1                          +                          AB                                                )                                            ⁢                                              (                                                                              B                            2                                                    +                                                      1                            /                            AB                                                                          )                                                                              ]                                                      =                          Γɛ              t                                      ,                            (        2        )            where t=tf+ts is the total thickness of the bilayer, a is the strain (unitless), B=tf/ts as defined before, and A=E′f/E′3 where E′ stands for the biaxial modulus of the material, while the function Γ=Γ(A,B) is implicitly defined. For a cantilever with fixed geometry then, a change in curvature Δκ is proportional to the change in strain Δε, which can be caused by different mechanisms. In the most common situation this is differential thermal expansion, in which case Δε=Δα ΔT, regardless of other considerations such as vibration tolerance, temperature sensitivity (Δκ/ΔT) can be increased by using a pair of materials with higher Δα, maximizing Γ, or—within practical limits—reducing the total cantilever thickness. This approach is adequate if the bi-material cantilever will be used as a thermal sensor. However, if the cantilever will instead be used as an actuator the amount of work it can perform becomes an issue and a different design compromise is needed. The restoring force at the cantilever tip (for rectangular section cantilevers) is proportional to the third power of its thickness. Selection of a pair of materials to maximize Δα implies a simultaneous selection of the elastic moduli, which fixes the A ratio. Since polymers have very low elastic moduli (E ˜1 GPa) the restoring force and the work performed in bending, both of which are proportional to the composite cantilever elastic modulus, will be low. Use of stiffer materials will allow exertion of larger forces, but then Δα, and hence Δε, will not be as high. It should be also clear that if (Δκ/ΔT) is small, large curvature changes (and therefore long displacements) may be obtained only by causing large temperature changes in the device. However, this option may not be satisfactory, since hot areas in a microdevice can lead to difficulties with heat transfer to surrounding areas, which can in turn require more complex designs.